A cPanel license is currently priced at $17.49 if it's just for your own access, and you can host as many domains as you want on that single account.
You didn't specify the resource requirements for each website, but a mid-sized VPS should meet your needs, typically available between $8 and $15.
Altogether, these options would cost you around $30 at the higher end.
Now, the next step is finding a reliable VPS provider within the $8 to $13 range, which is quite feasible given the number of options out there. Take some time to browse through the marketplace and evaluate the looking glass and latency for the shortlisted hosts. If the results look good, go ahead and purchase a VPS and cPanel license separately.
Make sure to maintain your current arrangements until you're fully confident that your new setup meets all your requirements. Remember, the new solution will centralize everything, creating a single point of failure for all your sites, whereas your existing setup likely has some level of redundancy, whether intentional or not.
As already mentioned, if you consider a free panel, then your budget can not only secure you a high-quality VPS but also a dedicated server from reputable providers like OVH or Hetzner.